SOLUTION: Hi. I'm home sick today. I'm trying to keep up with my algebra homework. My mom and I have both tried solving one of the problems, and we need help. WE've read the example over and

Question 221923: Hi. I'm home sick today. I'm trying to keep up with my algebra homework. My mom and I have both tried solving one of the problems, and we need help. WE've read the example over and over! The problem is:
-46 decreased by the difference between -23 and -61
The answer is -84. (looked it up in the back of the book) BUT we don't understand why?
We tried the following:
-46-(-23-61) but using the distributive property, seems like it would simplify to: -46+23+61 but that gives the wrong answer.
Can you please help us?? Thanks in advance!

Found 3 solutions by Alan3354, jim_thompson5910, likaaka:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
-46 decreased by the difference between -23 and -61
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The difference between -23 and -61 is 38. (-23 - (-61)) = 38
Decreasing -46 by 38 = -46 - 38 = -84
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Usually, "the difference" is assumed to be positive. For example,
the difference between 7 and 10 is 3. between 10 and 7 is also 3. Negatives are used only when it's specifically shown as a subtraction problem.
This problem is somewhat ambiguous.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
When they say "difference between -23 and -61", they mean the number of units from -23 to -61 (remember, 'difference' means subtraction). To find the number of units from any two points on a number line, you just subtract the two numbers. In this case, the difference of -23 and -61 is So -23 is 38 units away from -61 (go ahead and count it out if you don't believe me).

So this means that "-46 decreased by the difference between -23 and -61 " then becomes

OR....

Another way to do it is:

Either way, you get the same answer.

Answer by likaaka(51)   (Show Source): You can put this solution on YOUR website!
You're almost there, except that you want the DIFFERENCE between -23 and -61
So your equation will look like this
-46 - (-23 - -61)
Remember order of operations requires that the parenthesis be simplified first
-46 - (-23 - -61), simplify and note here that a minus of a minus is a plus
-46 - (-23 + 61)
-46 - (38), now here you technically distribute the negative into the parenthesis
-46-38
-84
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